On the detectability and observability of discrete-time Markov jump linear systems

This paper presents a new detectability concept for discrete-time Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper introduces a related observability concept which also generalizes previous concepts. Tests for detectability or observability are derived from the corresponding definitions, that can be perfomed in a finite number of steps. An illustrative example is included to show that a system may be detectable in the new sense but not in the MS sense.